Abstract
The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education. After describing the structure of the framework, several applications of inquiry-based learning in teaching numerical analysis and optimization are provided to illustrate the potential of the proposed framework. The framework is based on the Process of Scientific Inquiry (PoSI), while it consists of three pillars, each characterized by the use of a particular cognitive tool: Algorithm for presenting a list of steps to follow in order to solve a problem, CMAP software for constructing concept maps and MATLAB software for computer programming. In addition to this, a WebQuest Scenario can be used as an “auxiliary” cognitive tool by providing students with the opportunity to combine technology (e.g., MATLAB and CMAP software) with educational concepts (e.g., optimization), and to incorporate inquiry-based learning (i.e., PoSI). Introducing these cognitive tools to the design of the proposed didactic framework provides considerable potential of knowledge consolidation with reference to solving complex numerical problems using efficient algorithms.
Highlights
In recent years, the inquiry-based learning has received a great deal of attention from researchers who appear to focus mostly on the students’ engagement in active discovery learning and learning in environments that include characteristics of active participation, self-action, observation, exploration and experimentation (Psycharis, 2011; Kyriazis et al, 2009; Gormally et al, 2009; Richardson & Liang, 2008; Justice et al, 2007)
The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education
The framework is based on the Process of Scientific Inquiry (PoSI), while it consists of three pillars, each characterized by the use of a particular cognitive tool: Algorithm for presenting a list of steps to follow in order to solve a problem, CMAP software for constructing concept maps and MATLAB software for computer programming
Summary
The inquiry-based learning has received a great deal of attention from researchers who appear to focus mostly on the students’ engagement in active discovery learning and learning in environments that include characteristics of active participation, self-action, observation, exploration and experimentation (Psycharis, 2011; Kyriazis et al, 2009; Gormally et al, 2009; Richardson & Liang, 2008; Justice et al, 2007). Teaching Applied Mathematics in higher education based on the Process of Scientific Inquiry (PoSI) (National Institutes of Health, 2005) poses a challenge due to its multidisciplinary character (Lappas & Kritikos, 2015). This paper extends the work of Lappas and Kritikos (2015) by providing several applications of inquiry-based learning in teaching numerical analysis and optimization. A didactic framework based on the PoSI is presented for solving (a) nonlinear equations, (b) systems of linear equations and (c) constrained/unconstrained optimization problems. The aim of the framework is threefold: (i) to help students to understand the basic aspects of numerical analysis and optimization, (ii) to provide students with the opportunity to practice and refine their critical-thinking skills and (iii) to convey to students the purpose of scientific research.
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